Mathematics 'Nobel' rewards boundary-busting work

Elon Lindenstrauss was awarded the 2010 Fields medal for his results on measure rigidity in ergodic theory, and their applications to number theory

Cédric Villani was awarded the medal for his proofs of nonlinear Landau damping and convergence to equilibrium for the Boltzmann equation

Stanislav Smirnov was awarded the medal for the proof of conformal invariance of percolation and the planar Ising model in statistical physics

Ngô Bảo Châu was awarded the medal for for his proof of the fundamental lemma in the theory of automorphic forms through the introduction of new algebro-geometric methods

Four mathematicians this morning received the most prestigious award in their subject, the Fields medal, for work that helps unify the traditionally disparate fields of pure and applied mathematics.

The Fields medal is widely considered the mathematics equivalent of the Nobel prize and is awarded by the International Mathematical Union on the opening day of the International Congress of Mathematicians, which takes place every four years.

ICM 2010 kicked off today in Hyderabad, India, with the Indian president Prathibha Patil awarding the prizes. This time, all four medallists accepted, and remarked that their work helps demonstrate how the traditional distinction between pure and applied maths no longer holds.

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“The most interesting problems are on both sides of the division,” said one medallist, Elon Lindenstrauss, of the Hebrew University, Jerusalem.

From ergodic theory to soil

Aside from Lindenstrauss, this year’s winners were Ngô Bảo Châu of the University of Paris-South, France, Stanslav Smirnov of the University of Geneva, Switzerland, and Cédric Villani of the Henri Poincaré Institute, Paris, France.

In its explanation of its decision, the International Mathematical Union praised Lindenstrauss for his work on ergodic theory, which concerns dynamical systems that change over time and which originated as a branch of applied mathematics. His results have yielded important results in the completely different field of number theory, a branch of pure mathematics.

Ngô won for his proof of the fundamental lemma, a conjecture posed by Robert Langlands of the Institute of Advanced Study in Princeton, New Jersey. The conjecture is part of the “Langlands programme”, a collection of conjectures that aim to unify certain elements of algebra with number theory. US magazine Time included Ngô’s proof in its “Top Ten Scientific Discoveries of 2009″.

Smirnov’s area is mathematical physics. His award was given for highly theoretical work that touches on very practical problems, such as how water flows through soil.

Villani’s work is also related to physics, in particular the mathematical interpretation of the concept of entropy. He has applied this to solve long-standing problems, such as how fast the motions of gas particles converge to equilibrium.

Youth and age

The Fields medal is only awarded to mathematicians under 40, but that does not mean mathematicians only do their best work when young, said Smirnov. “I look forward to proving more theorems. I hope the weight of this prize doesn’t slow me down.”

When asked why mathematics has been so successful at finding applications in the real world, Villani – sporting a burgundy silk cravat and a palm-sized spider brooch – said&colon; “It is a very pleasant mystery. Let’s continue to enjoy it and explore.”

Also presented at the ICM today were three other awards, including the first ever Chern medal, for outstanding lifetime achievement in mathematics, which went to Louis Nirenberg, aged 85, of the Courant Institute of Mathematical Sciences in New York.

Meanwhile, the Nevanlinna prize, for contributions to information sciences, also awarded only to under-40s, was given to Daniel Spielman of Yale University. The Gauss prize for applied maths was won by Yves Meyer, aged 71, of the École Normale Supérieure de Cachan, France

Each Field’s winner receives a cash prize of CAN&dollar;15,000, which is a much smaller sum than the US&dollar;1 million or so given to Nobel laureates, or even the amount received by winners of the Chern medal, who get US&dollar;250,000 for themselves and another US&dollar;250,000 to donate to organisations that support mathematics.

Both the Nevanlinna and the Gauss prizes are worth €10,000 to their winners.